A sound source $(S)$ emits frequency of $180 H z$ when moving with velocity $5 m / s$ towards a moving wall moving with same speed as of source and a stationary observer $(O)$ hears the sound. The situation is shown in the diagram. Find the number of beats per second heard by the observer. $(speed of sound = 340 m / s)$

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Solution

Given,

Frequency of source $(S), n = 180 H Z$

Velocity of the source, $v_{s} = 5 m / s$

Direct frequency heard by the observer $(O)$ ,

$\Rightarrow n_{1} = n (\frac{v}{v + v_{s}})$

Since source and wall moving at same velocity, so, there is no relative motion between them. Therefore, frequency received by wall $= n .$

Frequency received by observer from wall,

$\Rightarrow n_{2} = n (\frac{v}{v + v_{s}})$

Beat frequency $= n_{1} - n_{2}$

$= n (\frac{v}{v + v_{s}}) - n (\frac{v}{v + v_{s}}) = 0$

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